Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.009 ) Pub Date : 2020-09-15 , DOI: 10.1017/prm.2020.72 Xin Zhong
We deal with an initial boundary value problem of nonhomogeneous Boussinesq equations for magnetohydrodynamics convection in two-dimensional domains. We prove that there is a unique global strong solution. Moreover, we show that the temperature converges exponentially to zero in H1 as time goes to infinity. In particular, the initial data can be arbitrarily large and vacuum is allowed. Our analysis relies on energy method and a lemma of Desjardins (Arch. Rational Mech. Anal. 137:135–158, 1997).